24. Correlation -0.015
How confident can you be?
I'm confident in -0.015 because it's closer to 0 than anything else, therefore has no correlation.
25. 25. A college football coach wants to know if there is a correlation between his players' leg strength and the time it takes for them to sprint 40 yards. He sets up the following and records the data.
Every day for a week: counts how many times each player leg press 350 lbs
following week: 40 yd sprint each day
Table shows average number of leg-press & yard dash time for 7 players
What is the equation of best fit?
How many seconds should be expect a player to take to run 40 yards if that player can do 22 leg-press repetitions? Round any values to the nearest tenth, if necessary.
Leg Press (reps) 15 - 18 - 8 - 30 - 26 - 12 - 21
40-yard Dash (s) 5.2 - 6.3 - 6.8 - 8.2 - 8.0 - 5.3 - 5.9
I'm not sure how to calculate the 40 yard dash
Don’t bother translating what he said, it was about some brand copying thingy. I just wasted a minute of my life
To calculate the equation of best fit (also known as the regression line) and predict the 40-yard dash time, you can use the method of linear regression. Here's how you can do it:
Step 1: Organize the data
Write down the given data in two separate columns: one for the number of leg press repetitions and another for the corresponding 40-yard dash times.
Leg Press (reps): 15 - 18 - 8 - 30 - 26 - 12 - 21
40-yard Dash (s): 5.2 - 6.3 - 6.8 - 8.2 - 8.0 - 5.3 - 5.9
Step 2: Calculate the correlation coefficient (r)
Before finding the equation of the best fit line, it's important to determine the strength and direction of the linear relationship between the two variables. The correlation coefficient (r) measures this relationship. You can calculate it using the following formula:
r = Σ((x - x̄)(y - ȳ)) / √((Σ(x - x̄)^2) * (Σ(y - ȳ)^2))
Where:
- Σ is the sum symbol
- x and y are the variables (number of leg press repetitions and 40-yard dash times respectively)
- x̄ is the mean of the x values
- ȳ is the mean of the y values
To calculate r, follow these steps:
- Calculate the mean (average) of both the number of leg press repetitions (x) and the 40-yard dash times (y) using the formula: x̄ = Σx / n and ȳ = Σy / n, where n is the number of data points (in this case, 7).
- Substitute the values into the correlation coefficient formula and calculate the numerator and denominator separately.
- Divide the numerator by the denominator and take the square root of the result to find r.
Once you've calculated the correlation coefficient (r), you would interpret its value to determine how strong and how related the leg strength and sprint time are. In this case, the closer to -1 or 1, the stronger the correlation.
Step 3: Find the equation of the best fit line
The equation of the best fit line can be determined using the formula: y = mx + b, where y is the predicted 40-yard dash time, x is the number of leg press repetitions, m is the slope of the line, and b is the y-intercept.
To calculate the slope (m):
- m = r * (sy / sx)
- r is the correlation coefficient calculated in Step 2
- sy is the standard deviation of the 40-yard dash times
- sx is the standard deviation of the number of leg press repetitions
To calculate the y-intercept (b):
- b = ȳ - m * x̄
Calculate the slope and y-intercept based on the above formulas to find the equation of the best fit line.
Step 4: Predict the 40-yard dash time
Once you have the equation of the best fit line, you can substitute the given number of leg press repetitions (22 in this case) into the equation and solve for the predicted 40-yard dash time.
By following these steps, you can determine the equation of the best fit line and predict the 40-yard dash time for a player who can do 22 leg-press repetitions.
In problems of this type, it is easier if you could make a scatter plot (or dot-plot) of the data before starting the calculations.
In case you spot an outlier, you will have to occasion of excluding it before you do the calculations.
In the given data, I suspect there is an outlier, but if you have not learned about the criteria of eliminating an outlier before, you can just ignore it.
Do you have a graphing calculator?
If you're expected to find the regression line (equation of best fit) with it, then try the calculator. If you don't know how to operate it, post the make and model of the calculator. Perhaps someone can help.
If you have learned to find the equation of best by graphing, then graph it first, and then draw a line as close to most points as possible and determine the equation.